So close to solving! please help - force/friction

A mass m1 on a horizontal shelf is attached by a thin string that passes over a frictionless pulley to a 3.0 kg mass (m2) that hangs over the side of the shelf 1.3 m above the ground. The system is released from rest at t = 0 and the 3.0 kg mass strikes the ground at t = 0.78 s. The system is now placed in its initial position and a 1.2 kg mass is placed on top of the block of mass m1. Released from rest, the 3.0 kg mass now strikes the ground 1.3 seconds later.
(a) Determine the mass m1.
kg

(b) Determine the coefficient of kinetic friction between m1 and the shelf.

I did that and ended up with quadratic equations and I plug that in the formula and ended up with a value for M1. When I plug in M1 to the 2 Uk equations, they did not match.

When you put the above into standard form for a quadratic you might have made an error. I would have solved the first for Uk, as you did, but then plugged that into the second equation to solve for M1.

I finally got it!!! After so much math crunching and leaving all the decimal places as they are have paid off. Thank you Doc for the advice of redoing the numbers.
It is always sweeter when you solve a problem all by your self(with exception of your help teehee). Thanks!